--- Barkley Vowk <bvowk@math.ualberta.ca> wrote: >
> On Mon, 28 Apr 2003, Paul Hughes wrote:
>
> > In the last 20 years I have yet to see a single
> major
> > advance on the nature of the universe not fit
> within
> > my intuitional insights of how I suspected the
> > universe works.
> >
> > Intution alone may not solve the problem, but in
> cases
> > like this it has always leads me in the right
> > direction, which in turn was invariably and
> logically
> > demonstrated by myself or others.
>
> Given your training, I'd say it would be impossible
> to separate your
> "intuition" from your training the in current models
> and ability to reason
> within that framework. It seems obvious that the
> universe fits your models
> when you think "through" those models. This would be
> valid if the universe
> was intuitive to a child, not to a man who digests
> and applies
> mathematical models to the universe for a living.

Intuition is more subtle than simple training using
given models since it is the thing which allows us to
leap from our normal models (the models which we have
been trained in) to new, entirely different and
unexpected models. It is the way we enter new
territory and navigate the totally unexplored regions
of the mentally-accessible metaspace. Mathematicians
are more like explorers than inventors since they are
able to "discover" these new areas of external reality
and new types of alien platonic forms, this is the
essence of creativity in mathematics and it is exactly
what intuition is all about: transcending, the ability
to go beyond current perceptions and perceived models,
to percieve a deeper richer reality in a clearer and
broader context than had previously been imagined.